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The point of intersection of the lines r → = 7 i ˙ ^ + 10 j ˙ ^ + 13 k ^ + s ( 2 i ˙ ^ + 3 j ˙ ^ + 4 k ^ ) and r → = 3 i ˙ ^ + 5 j ˙ ^ + 7 k ^ + t ( i ˙ ^ + 2 j ˙ ^ + 3 k ^ ) is

Options

  1. Ai ˙ ^ + j ˙ ^ - k ^
  2. B2 i ˙ ^ - j ˙ ^ + 4 k ^
  3. Ci ˙ ^ - j ˙ ^ + k ^
  4. Di ˙ ^ + j ˙ ^ + k ^

Correct answer

D. i ˙ ^ + j ˙ ^ + k ^

Step-by-step solution

Two given lines intersect, if 7 i ˙ ^ + 10 j ˙ ^ + 13 k ^ + s 2 i ˙ ^ + 3 j ˙ ^ + 4 k ^ = 3 i ˙ ^ + 5 j ˙ ^ + 7 k ^ + t ( i ˙ ^ + 2 j ˙ ^ + 3 k ^ ) ⟹ 7 + 2 s i ˙ ^ + 10 + 3 s j ˙ ^ + ( 13 + 4 s ) k ^ = 3 + t i ˙ ^ + 5 + 2 t j ˙ ^ + ( 7 + 3 t ) k ^ ⟹ 7 + 2 s = 3 + t ⟹ 2 s - t = - 4 ...(i) 10 + 3 s = 5 + 2 t ⟹ 3 s - 2 t = - 5 ...(ii) a n d   13 + 4 s = 7 + 3 t ⟹ 4 s - 3 t = - 6 ...(iii) On solving Eqs. (i) and (iii), w

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